arXiv subjects

Yosief Wondmagegne

Publications and source records attributed to Yosief Wondmagegne.

6 recordsLinked to original sources

arXiv2024

Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results

This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its speed. This situation is usually referred to in the literature as moving-boundary problem with kinetic condition. As a direct application, we propose a numerical scheme to forecast the penetration of small diffusants into a rubber-based material. To check the quality of our results, we compare the numerical results obtained by global random walks either using the analytical solution to selected benchmark cases or relying on finite element approximations with a priori known convergence rates. It turns out that the global random walk concept can be used to produce good quality approximations of the weak solutions to the target class of problems.

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arXiv2023

Random walks and moving boundaries: Estimating the penetration of diffusants into dense rubbers

For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. In this paper, we propose a random walk algorithm able to lead to good numerical approximations of both the concentration profile and the location of the sharp front. Essentially, the proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to results based on a finite element approach with a controlled convergence rate. Our numerical experiments recover well penetration depth measurements of an experimental setup targeting dense rubbers.

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arXiv2022

Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants

We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with the backward Euler method for the time discretization. Besides dealing with the existence and uniqueness of solution to the fully discrete problem, we derive a \textit{a priori} error estimate for the mass concentration of the diffusants, and respectively, for the position of the moving boundary. Numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.

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arXiv2022

Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber

We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.

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arXiv2020

A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements

We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling in a piece of material made of ethylene propylene diene monomer rubber (EPDM). The main challenge is to find out relatively simple model components which can mimic the mechanical behavior of the rubber. Such special structure is identified here so that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We investigate two cases: a dense rubber and a rubber foam, both made of the same matrix material. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the \textit{a priori} unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large-time behavior of the material.

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arXiv2019

Modelling, Simulation and Parameter Identification of Active Pollution Reduction with Photovoltaic Asphalt

We develop and implement a numerical model to simulate the effect of photovoltaic asphalt on reducing the concentration of nitrogen monoxide due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a parameter estimation process that can be used to find missing parameters, and finally, we train and compare this simulation with different data sets. We analyze the results and provide an outlook on further research.

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